Add different textures to front and back of plane with solidify?
There was only one image in the file, so I substituted a Diffuse BSDF for the second image. There are two options you have now.

Option 1

The reason that the Geometry > Backfacing did not appear to work was because that the Solidify modifier made it so that the map/diffuse went inside the map.

An exaggerated Solidify:



The solution if you want to keep the Solidify modifier goes like this. Apply all modifiers. Use the steps in Add different materials to different parts of a mesh? to apply the other image/diffuse to the non-map faces.

Option 2

Solution produced with Option 2 (low-res; 20 samples):



This is the better solution. Since the Solidify modifier does next to nothing, delete it, and the original node setup will work. The two Diffuse BSDF's outputs are crossed just because it needed to be inverted. I'm sure you understand.



The following .blend file produced the result at the top of Option 2.